Average Error: 29.5 → 0.2
Time: 11.4s
Precision: 64
Internal precision: 128
\[\sqrt{x + 1.0} - \sqrt{x}\]
⬇
\[\frac{1.0}{\sqrt{x + 1.0} + \sqrt{x}}\]

Error

Bits error versus x

Target

Original29.5
Comparison0.2
Herbie0.2
\[ \frac{1.0}{\sqrt{x + 1.0} + \sqrt{x}} \]

Derivation

  1. Initial program 29.5

    \[\sqrt{x + 1.0} - \sqrt{x}\]
  2. Using strategy rm

  3. Applied flip-- 29.3

    \[\leadsto \color{blue}{\frac{{\left(\sqrt{x + 1.0}\right)}^2 - {\left(\sqrt{x}\right)}^2}{\sqrt{x + 1.0} + \sqrt{x}}}\]

  4. Applied simplify 0.2

    \[\leadsto \frac{\color{blue}{1.0}}{\sqrt{x + 1.0} + \sqrt{x}}\]
  5. Removed slow pow expressions

Runtime

Time bar (total: 11.4s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(2622523767 1900855601 2796833090 3739975971 2955515552 884437260)'
(FPCore (x)
  :name "Main:bigenough3 from C"

  :target
  (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

  (- (sqrt (+ x 1.0)) (sqrt x)))